A Primer on Portfolio Theory

Bernd Scherer

1.1 MEAN–VARIANCE-BASED PORTFOLIO CONSTRUCTION

The theory of mean–variance-based portfolio selection is a cornerstone of modern asset management.¹¹The reader is assumed to be familiar with the basics of mean–variance optimisation. Aconcise review can be found in Elton and Gruber (1995). This chapter will focus on selected issues not commonly found in textbooks. It rests on the presumption that rational investors choose among risky assets purely on the basis of expected return and risk, with risk measured as variance. In this case a portfolio is considered mean–variance efficient if it minimises the variance for a given expected mean return or if it maximises the expected mean return for a given variance. Mean–variance efficiency rests on firm theoretical grounds if either

• investors exhibit quadratic utility – in which case they ignore non-normality in the data²²Discussions of the theory of utility can be found in Gollier (2001). Quadratic utility is of the form

  $$u\left( w \right) = w - \frac{1}{2}bw2$$ , where u(w) expresses utility, a measure of happiness, as a function of uncertain wealth, w. In this example greater utility is not strictly an increase in wealth as